Mathematical word-problems: where do I start?
Many children find mathematical word-problems challenging, even those who are competent mathematicians. The main difficulty is how to approach the problem; this involves deciding which mathematical operation to use and where to start the problem-solving process. In this blog post I will explore these aspects of mathematical word-problems and look at ways to help children develop their word-problem solving skills, which will help give them more confidence to use their existing mathematical abilities.
Deciding which mathematical operation to use
For many children the decision whether to add, subtract, multiply or divide is a major stumbling block when approaching word-problems. This is compounded by the number of words used in questions, many of which simply set the scene without any relevance to the mathematical process required to find a solution. For example,
Lewis and Lydia went to a school fayre. Lydia took £4.50 and Lewis had £3.75. Lydia bought a chocolate bar for 80p and a drink for £1.00. Lewis spent his money on a game, which cost £1.50. What was the total amount of money they spent? If they put their change altogether what did they have left?
In this example a strategy would be to underline the key mathematical elements, which are the monetary amounts and the words ‘total’, ‘spent’, ‘altogether’ and ‘left’. This helps to identify the numbers involved (after all, any number in a mathematical word-problem will be relevant) and which mathematical operation(s) to use.
Break down the problem
It is important with multi-step word-problems to isolate each part of the question, then to approach the parts sequentially. In the Lewis and Lydia example there are three steps: we need to add the amounts taken to the fayre by Lewis and Lydia; we need to calculate how much they spend altogether (which involves adding Lydia’s two amounts to Lewis’s one purchase); finally we need to subtract their joint expenditure from the initial total. To help a child to identify these steps and put them in order I suggest that the child writes down the calculations needed:
£4.50 + £3.75 =
£1.00 + 80p + £1.50 =
£8.25 – £3.30 =
Now let’s look at other ways to help a child develop word-problem solving skills.
Visualise the problem
Some children learn more effectively using a visual learning style, rather than written. For these children it can help to draw the problem. For example, a question might ask, “How many Easter eggs will I need if I invite four friends to my party and give them each a bag containing six eggs?” To approach this a child could draw six bags with four eggs in each. This will help a child to visually recognise that it is a multiplication problem. This strategy can be applied to questions involving other mathematical operations, for example, “If I have a two-litre jug of milk and pour drinks into three 250ml cups how much milk is left in the jug?” Before drawing the jug and cups it is important to identify that different units of measurement have been used, therefore the first step is to put both the milk in the jug and the milk in the cups into the same unit (I suggest millilitres because litres would involve calculating using decimal points, which many children find tricky).
When helping a child to practise word-problems try to motivate him or her by setting the problem in a relevant everyday situation to which he or she can easily relate (this will engage the child in the problem and help him or her to remember the process). If a child enjoys Star Wars then give any characters in the question a name from the series. If a child enjoys helping in the kitchen then use a problem involving cooking ingredients (the possibilities are endless).
Fast recall of number facts
To help a child solve word-problems quickly it is vital that he or she knows basic number facts, such as addition/subtraction to twenty, doubles/halves and times tables. Regular practise of these avoids a child needing to spend time on a calculation process which should be part of their automatic number knowledge.
Clearly word-problems require reading, and the length of some problems involves several sentences. Furthermore, the complexity of some word-problems can involve many stages to put in order, which requires retaining much information. I have emphasised the significance of reading in my earlier blog (How can I help my child with reading?) and solid comprehension skills are definitely an asset when attempting word-problems as they help a child to read the question at a good pace and understand its nature.
A useful acronym to help remember many of the techniques discussed in this blog is:
Comprehension (efficient reading and recall) Operation (whether to add, subtract, multiply or divide) Meaningful (relevant, everyday situations) Break-down (segment the problem then sequence it) See (visualise the problem)